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We investigate the phase transitions in a one-dimensional system with colored noise. Previous studies indicated that the phase diagram of this system included extended and disorder-induced localized phases. However, by studying the properties of wave functions, we find that this phase diagram can be further refined, revealing the existence of a bound phase for the large potential amplitude $W$ and noise control parameter $\alpha$. In the bound phase, the wave function cannot extend throughout the entire chain, tails decay faster than exponentially and its distribution expands as the system size increases. By adjusting the potential amplitude to induce a transition from the extended phase to the bound phase, we find that bound states coexist with extended states in the spectrum. In contrast, when the system transitions from the Anderson localized phase to the bound phase, we do not observe the obvious coexistence of Anderson localized and bound states. Finally, by performing the time evolution, we find that the dynamic transition point of the bound phase is inconsistent with the static one for large $\alpha$., Comment: 10 pages, 12 figures, To be published in Physical Review B

Few-body physics for anyons has been intensively studied within the anyon-Hubbard model, including the quantum walk and Bloch oscillations of two-anyon states. However, the known theoretical proposal and experimental simulations of two-anyon states in one-dimensional lattice have been carried out by expanding the wavefunction in terms of non-orthogonal basis vectors, which introduces extra non-physical degrees of freedom. In the present work, we deduce the finite difference equations for the two-anyon state in the one-dimensional lattice by solving the Schr\"odinger equation with orthogonal basis vectors. Such an orthogonal scheme gives all the orthogonal physical eigenstates for the time-independent two-anyon Schr\"odinger equation, while the conventional (non-orthogonal) method produces a lot of non-physical redundant eigen-solutions whose components violate the anyonic relations. The dynamical property of the two-anyon states in a sufficiently large lattice has been investigated and compared in both the orthogonal and conventional schemes, which proves to depend crucially on the initial states. When the initial states with two anyons on the same site or (next-)neighboring sites are suitably chosen to be in accordance with the anyonic coefficient relation, we observe exactly the same dynamical behavior in the two schemes, including the revival probability, the probability density function, and the two-body correlation, otherwise, the conventional scheme will produce erroneous results which not any more describe anyons. The period of the Bloch oscillation in the pseudo-fermionic limit is found to be twice that in the bosonic limit, while the oscillations disappear for statistical parameters in between. Our findings are vital for quantum simulations of few-body physics with anyons in the lattice., Comment: 11 pages, 9 figures

The collisional dynamics of two symmetric droplets with equal intraspecies scattering lengths and particle number density for each component is studied by solving the corresponding extended Gross-Pitaevskii equation in two dimensions by including a logarithmic correction term in the usual contact interaction. We find the merging droplet after collision experiences a quadrupole oscillation in its shape and the oscillation period is found to be independent of the incidental momentum for small droplets. With increasing collision momentum the colliding droplets may separate into two, or even more, and finally into small pieces of droplets. For these dynamical phases, we manage to present boundaries determined by the remnant particle number in the central area and the damped oscillation of the quadrupole mode. A stability peak for the existence of droplets emerges at the critical particle number $N_c \simeq 48$ for the quasi-Gaussian and flat-top shapes of the droplets., Comment: 7 pages, 4 figures

Most existing 6-DoF robot grasping solutions depend on strong supervision on grasp pose to ensure satisfactory performance, which could be laborious and impractical when the robot works in some restricted area. To this end, we propose a self-supervised 6-DoF grasp pose detection framework via an Augmented Reality (AR) teleoperation system that can efficiently learn human demonstrations and provide 6-DoF grasp poses without grasp pose annotations. Specifically, the system collects the human demonstration from the AR environment and contrastively learns the grasping strategy from the demonstration. For the real-world experiment, the proposed system leads to satisfactory grasping abilities and learning to grasp unknown objects within three demonstrations.

The study of integrable systems has led to significant advancements in our understanding of many-body physics. We design a series of numerical experiments to analyze the integrability of a mass-imbalanced two-body system through energy level statistics and deep learning of wavefunctions. The level spacing distributions are fitted by a Brody distribution and the fitting parameter $\omega$ is found to separate the integrable and non-integrable mass ratios by a critical line $\omega=0$. The convolutional neural network built from the probability density images could identify the transition points between integrable and non-integrable systems with high accuracy, yet in a much shorter computation time. A brilliant example of the network's ability is to identify a new integrable mass ratio $1/3$ by learning from the known integrable case of equal mass, with a remarkable network confidence of $98.78\%$. The robustness of our neural networks is further enhanced by adversarial learning, where samples are generated by standard and quantum perturbations mixed in the probability density images and the wavefunctions, respectively., Comment: 14 pages,16 figures

The collective excitation modes in quantum droplets trapped in a two-dimensional harmonic potential in the context of symmetric weakly interacting binary bosonic mixtures are studied. By utilizing the linearization technique, the time-dependent extended Gross-Pitaevskii equation, and a sum-rule approach with a variational approximation, the ground state properties and collective excitations of such a two-dimensional quantum system are investigated for various system parameters. We present comprehensive analysis and calculations on the effect of the confinement strength and anisotropy of the trapping potential, the number of atoms in the droplet, and the collective excitation modes. The radius of the droplet, as well as the chemical potential, is non-monotonically related to the number of atoms in the droplet, and the confinement tends to shift the minimum values towards the ideal gas limit. The excitation frequency peaks, which are prominent in a self-bounded droplet, become less pronounced and smoother when subjected to a strong trapping potential. The sum-rule approach fails to reproduce the breathing mode frequency for a moderate number of atoms in a weak trapping potential, however, works perfectly well in a strong confinement. It was found that the anisotropy in the trap eliminates the degeneracy between the quadrupole and scissors modes that occurs in an isotropic trap, causing the frequencies of these two modes to immediately diverge from each other for any degree of anisotropy. These findings provide valuable insights into the unique characteristics and behavior of quantum droplets, offering potential implications for future research and applications in the dynamic behaviors of intriguing quantum droplets., Comment: 12 pages, 6 figures

Quasi-one-dimensional (Q1D) Cr-based pnictide K$_2$Cr$_3$As$_3$ has aroused great research interest due to its possible triplet superconducting pairing symmetry. Recent experiments have shown that incorporating hydrogen atoms into K$_2$Cr$_3$As$_3$ would significantly change its electronic and magnetic properties. Hence, it's necessary to investigate the impact of hydrogen doping in superconducting pairing symmetry of this material. Employing the hydrogen as an non-trivial electron-doping, our calculates show that, different from the $p_z$-wave obtained without hydrogen, the system exhibits $p_x\pm ip_y$ pairing superconductivity under specific hydrogen doping. Specifically, we adopt the random-phase-approximation approach based on a six-band tight-binding model equipped with multi-orbital Hubbard interactions to study the hydrogen-doping dependence of the pairing symmetry and superconducting $T_c$. Under the rigid-band approximation, our pairing phase diagram shows the spin-triplet pairing states is dominated through out the hydrogen-doping regime $x\in (0,0.7)$. Particularly, the $T_c\sim x$ curve shows a peak at the 3D-quasi-1D Lifshitz transition point, and the pairing symmetry around this doping level is $p_x\pm ip_y$. The physical origin of this pairing symmetry is that the density of states is mainly concentrated at $k_x(k_y)$ with large momentum. Due to the three-dimensional character of the real material, this $p_x\pm ip_y$-wave superconducting state possesses point gap nodes. We further provide experiment prediction to identify this triplet $p_x\pm ip_y$-wave superconductivity., Comment: 9 pages,9 figures. arXiv admin note: substantial text overlap with arXiv:2111.14367

We study the stationary and excitation properties of a one-dimensional quantum droplet in the two-component Bose mixture trapped in a harmonic potential. By constructing the energy functional for the inhomogeneous mixture, we elaborate the extended the Gross-Pitaevskii equation applicable to both symmetric and asymmetric mixtures into a universal form, and the equations in two different dimensionless schemes are in a duality relation, i.e. the unique parameters left are inverse of each other. The Bogoliubov equations for the trapped droplet are obtained by linearizing the small density fluctuation around the ground state and the low-lying excitation modes are calculated numerically.It is found that the confinement trap changes easily the flat-top structure for large droplets and alters the mean square radius and the chemical potential intensively. The breathing mode of the confined droplet connects the self-bound and ideal gas limits, with the excitation in the weakly interacting Bose condensate for large particle numbers lying in between. We explicitly show how the continuum spectrum of the excitation is split into discrete modes, and finally taken over by the harmonic trap. Two critical particle numbers are identified by the minimum size of the trapped droplet and the maximum breathing mode energy, both of which are found to decrease exponentially with the trapping parameter., Comment: 11 pages, 7 figures

We investigate a single-particle in one-dimensional Wannier-Stark ladders with either a linear potential or a mosaic potential with spacing $\kappa=2$. In both cases, we exactly determine the critical energies separating the weakly ergodic states from ergodic states for a finite potential height. Especially in the latter case, we demonstrate a rich phase diagram with ergodic states, weakly ergodic states, and strongly Wannier-Stark localized states. Our results also exhibit that critical energies are highly dependent on the height of the ladder and ergodic states only survive at $E\approx0$ for the high ladder. Importantly, we find that the number of ergodic states can be adjusted by changing the interval of the non-zero potential. These interesting features will shed light on the study of disorder-free systems., Comment: 10 pages, 12 figures, accepted by physical review A

We study the topology and localization properties of a generalized Su-Schrieffer-Heeger (SSH) model with a quasi-periodic modulated hopping. It is found that the interplay of off-diagonal quasi-periodic modulations can induce topological Anderson insulator (TAI) phases and reentrant topological Anderson insulator (RTAI), and the topological phase boundaries can be uncovered by the divergence of the localization length of the zero-energy mode. In contrast to the conventional case that the TAI regime emerges in a finite range with the increase of disorder, the TAI and RTAI are robust against arbitrary modulation amplitude for our system. Furthermore, we find that the TAI and RTAI can induce the emergence of reentrant localization transitions. Such an interesting connection between the reentrant localization transition and the TAI/RTAI can be detected from the wave-packet dynamics in cold atom systems by adopting the technique of momentum-lattice engineering., Comment: 13 pages, 13 figures

We present a method for reproducing complex multi-character interactions for physically simulated humanoid characters using deep reinforcement learning. Our method learns control policies for characters that imitate not only individual motions, but also the interactions between characters, while maintaining balance and matching the complexity of reference data. Our approach uses a novel reward formulation based on an interaction graph that measures distances between pairs of interaction landmarks. This reward encourages control policies to efficiently imitate the character's motion while preserving the spatial relationships of the interactions in the reference motion. We evaluate our method on a variety of activities, from simple interactions such as a high-five greeting to more complex interactions such as gymnastic exercises, Salsa dancing, and box carrying and throwing. This approach can be used to ``clean-up'' existing motion capture data to produce physically plausible interactions or to retarget motion to new characters with different sizes, kinematics or morphologies while maintaining the interactions in the original data., Comment: 11 pages. Accepted to SIGGRAPH 2023

In-hand object manipulation is challenging to simulate due to complex contact dynamics, non-repetitive finger gaits, and the need to indirectly control unactuated objects. Further adapting a successful manipulation skill to new objects with different shapes and physical properties is a similarly challenging problem. In this work, we show that natural and robust in-hand manipulation of simple objects in a dynamic simulation can be learned from a high quality motion capture example via deep reinforcement learning with careful designs of the imitation learning problem. We apply our approach on both single-handed and two-handed dexterous manipulations of diverse object shapes and motions. We then demonstrate further adaptation of the example motion to a more complex shape through curriculum learning on intermediate shapes morphed between the source and target object. While a naive curriculum of progressive morphs often falls short, we propose a simple greedy curriculum search algorithm that can successfully apply to a range of objects such as a teapot, bunny, bottle, train, and elephant., Comment: Published as a conference paper at EuroGraphics 2023

In the usual perception, surface superconductivity is associated with the surface nucleation of a superconducting condensate above the upper critical field in type-II superconductors or with a rearrangement of phonon properties and the electron-phonon coupling near surfaces/interfaces. Recently, it has been found that there is another example when the surface superconducting temperature is increased up to 20-25% as compared to the bulk one due to constructive interference of superconducting pair states. In the present work, we demonstrate that in fact, such an interferenceinduced enhancement can be much more pronounced, up to nearly 70%. Furthermore, here it is shown that such an interference enhancement persists over a wide range of microscopic parameters.

Local gauge symmetry is intriguing for the study of quantum thermalization breaking. For example, in the high-spin lattice Schwinger model (LSM), the local U(1) gauge symmetry underlies the disorder-free many-body localization (MBL) dynamics of matter fields. This mechanism, however, would not work in a spin-1/2 LSM due to the absence of electric energy in the Hamiltonian. In this paper, we show that the spin-1/2 LSM can also exhibit disorder-free MBL dynamics, as well as entropy prethermalization, by introducing a four-fermion interaction into the system. The interplay between the fermion interaction and U(1) gauge symmetry endows the gauge fields with an effectively disordered potential which is responsible for the thermalization breaking. It induces anomalous (i.e., non-thermal) behaviors in the long-time evolution of such quantities as local observables, entanglement entropy, and correlation functions. Our work offers a new platform to explore emergent non-thermal dynamics in state-of-the-art quantum simulators with gauge symmetries.

The extended quantum Rabi models make a significant contribution to understand the quantum nature of the atom-light interaction. We transform two kinds of extended quantum Rabi model, anisotropic Rabi model and asymmetric Rabi model, into rotating frame, and regard them as periodically driven quantum systems. The analytical solutions of the quasi-energy spectrum as well as the Floquet modes for both models are constructed by applying the Floquet theory and the high-frequency expansion, which is applied to the non-stroboscopic dynamics of physical observables such as atomic inversion, transverse magnetization, atom-field correlation, etc. For anisotropic Rabi model, the quasi energy fits well with the numerical results even when the rotating-wave coupling is in the deep-strong coupling regime $g\simeq\hbar\omega$ if the counterrotating terms is small enough compared to the driving frequency. Avoided level crossing may occur for quasi energy with the same parity when the positive branch spectrum lines for the total excitation number $N$ cross the negative branch lines for $N+2$, while the high frequency expansion fails to predict this due to the conservation of the total excitation number. Furthermore, we present analytical and numerical study of the long-time evolution of population and figure out the analytical method is credible for the population dynamics. For asymmetric Rabi model, we find that the external bias field which breaks the parity symmetry of total excitation number tends to cluster the upper and lower branches into two bundles, and the detuning induced gap in the first temporal Brillouin zone shows a quadratic dependence on the bias. Both models prove that treating the Hamiltonian in the rotating frame by Floquet theory gives an alternative tool in the study of interaction between atom and light., Comment: 11 pages, 6 figures

We study the localization transition in periodically driven one-dimensional non-Hermitian lattices where the piece-wise two-step drive is constituted by uniform coherent tunneling and incommensurate onsite gain and loss. We find that the system can be in localized, delocalized, or mixed-phase depending on the driving frequency and the phase shift of complex potential. Two critical driving frequencies of the system are identified, the first one corresponds to the largest phase shift of the complex potential so that the quasi-energy spectrum is still real and all the states are extended, the second one corresponds to the disappear of full real spectrum, and very weak complex potential leads to the emergence of localized states when the driving frequency is lower than this critical frequency. In the high frequency limit, we find the critical phase shift that separates the two regions with respectively real and complex spectrum tends to a constant value that can be captured by an effective non-Hermitian Hamiltonian.

We uncover the relationship of topology and disorder in a one-dimensional Su-Schrieffer-Heeger chain subjected to a slowly varying quasi-periodic modulation. By numerically calculating the disorder-averaged winding number and analytically studying the localization length of the zero modes, we obtain the topological phase diagram, which implies that the topological Anderson insulator (TAI) can be induced by a slowly varying quasi-periodic modulation. Moreover, unlike the localization properties in the TAI phase caused by random disorder, mobility edges can enter into the TAI region identified by the fractal dimension, the inverse participation ratio, and the spatial distributions of the wave functions, the boundaries of which coincide with our analytical results., Comment: 9 pages, 8 figures

We present a method of training character manipulation of amorphous materials such as those often used in cooking. Common examples of amorphous materials include granular materials (salt, uncooked rice), fluids (honey), and visco-plastic materials (sticky rice, softened butter). A typical task is to spread a given material out across a flat surface using a tool such as a scraper or knife. We use reinforcement learning to train our controllers to manipulate materials in various ways. The training is performed in a physics simulator that uses position-based dynamics of particles to simulate the materials to be manipulated. The neural network control policy is given observations of the material (e.g. a low-resolution density map), and the policy outputs actions such as rotating and translating the knife. We demonstrate policies that have been successfully trained to carry out the following tasks: spreading, gathering, and flipping. We produce a final animation by using inverse kinematics to guide a character's arm and hand to match the motion of the manipulation tool such as a knife or a frying pan.

We investigate quantum dynamics of a quantum walker on a finite bipartite non-Hermitian lattice, in which the particle can leak out with certain rate whenever it visits one of the two sublattices. Quantum walker initially located on one of the non-leaky sites will finally totally disappear after a length of evolution time and the distribution of decay probability on each unit cell is obtained. In one regime, the resultant distribution shows an expected decreasing behavior as the distance from the initial site increases. However, in the other regime, we find that the resultant distribution of local decay probability is very counterintuitive, in which a relatively high population of decay probability appears on the edge unit cell which is the farthest from the starting point of the quantum walker. We then analyze the energy spectrum of the non-Hermitian lattice with pure loss, and find that the intriguing behavior of the resultant decay probability distribution is intimately related to the existence and specific property of edge states, which are topologically protected and can be well predicted by the non-Bloch winding number. The exotic dynamics may be observed experimentally with arrays of coupled resonator optical waveguides., Comment: 7 pages, 8 figures

We study the spin squeezing in a spin-1/2 Bose-Einstein condensates (BEC) with Raman induced spin-orbit coupling (SOC). Under the condition of two-photon resonance and weak Raman coupling strength, the system possesses two degenerate ground states, using which we construct an effective two-mode model. The Hamiltonian of the two-mode model takes the form of the one-axis-twisting Hamiltonian which is known to generate spin squeezing. More importantly, we show that the SOC provides a convenient control knob to adjust the spin nonlinearity responsible for spin squeezing. Specifically, the spin nonlinearity strength can be tuned to be comparable to the two-body density-density interaction, hence is much larger than the intrinsic spin-dependent interaction strength in conventional two-component BEC systems such as $^{87}$Rb and $^{23}$Na in the absence of the SOC. We confirm the spin squeezing by carrying out a fully beyond-mean-field numerical calculation using the truncated Wigner method. Additionally, the experimental implementation is also discussed., Comment: 8 pages, 4 figures

The (pseudo-)spin degrees of freedom greatly enriches the physics of cold atoms. This is particularly so for systems with high spins (i.e., spin quantum number larger than 1/2). For example, one can construct not only the rank-1 spin vector, but also the rank-2 spin tensor in high spin systems. Here we propose a simple scheme to couple the spin tensor and the center-of-mass orbital angular momentum in a spin-1 cold atom system, and show that this leads to a new quantum phase of the matter: the spin-nematic vortex state that features vorticity in an SU(2) spin-nematic tensor subspace. Under proper conditions, such states are characterized by quantized topological numbers. Our work opens up new avenues of research in topological quantum matter with high spins.

Due to the boundary coupling in a finite system, the zero modes of a standard Su-Schrieffer-Heeger (SSH) model may deviate from exact-zero energy. A recent experiment has shown that by increasing the system size or altering gain or loss strength of the SSH model with parity-time ($\mathcal{PT}$) symmetry, the real parts of the energies of the edge modes can be recovered to exact-zero value [Song \emph{et al.} Phys. Rev. Lett. \textbf{123}, 165701 (2019)]. To clarify the effects of $\mathcal{PT}$-symmetric potentials on the recovery of the nontrivial zero modes, we study the SSH model with $\mathcal{PT}$-symmetric potentials of different forms in both infinite and finite systems. Our results indicate that the energies of the edge modes in the infinite size case decide whether or not the success of the recovery of the zero modes by tuning the strength of $\mathcal{PT}$-symmetric potential in a finite system. If the energies of the edge modes amount to zero in the thermodynamic limit under an open boundary condition (OBC), the recovery of the zero modes will break down by increasing the gain or loss strength for a finite system. Our results can be easily examined in different experimental platforms and inspire more insightful understanding on nontrivial edge modes in topologically non-Hermitian systems., Comment: 12 pages, 11 figures

This paper investigates the hedging performance of pegged foreign exchange market in a regime switching (RS) model introduced in a recent paper by Drapeau, Wang and Wang (2019). We compare two prices, an exact solution and first order approximation and provide the bounds for the error. We provide exact RS delta, approximated RS delta as well as mean variance hedging strategies for this specific model and compare their performance. To improve the efficiency of the pricing and calibration procedure, the Fourier approach of this regime-switching model is developed in our work. It turns out that: 1 -- the calibration of the volatility surface with this regime switching model outperforms on real data the classical SABR model; 2 -- the Fourier approach is significantly faster than the direct approach; 3 -- in terms of hedging, the approximated RS delta hedge is a viable alternative to the exact RS delta hedge while significantly faster.

The degenerate Bose-Fermi (BF) mixtures in one dimension present a novel realization of two decoupled Luttinger liquids with bosonic and fermionic degrees of freedom at low temperatures. However, the transport properties of such decoupled Luttinger liquids of charges have not yet been studied. Here we apply generalized hydrodynamics to study the transport properties of one-dimensional (1D) BF mixtures with delta-function interactions. The initial state is set up as the semi-infinite halves of two 1D BF mixtures with different temperatures, joined together at the time $t=0$ and the junction point $x=0$. Using the Bethe ansatz solution, we first rigorously prove the existence of conserved charges for both the bosonic and fermionic degrees of freedom, preserving the Euler-type continuity equations. We then analytically obtain the distributions of the densities and currents of the local conserved quantities which solely depend on the ratio $\xi=x/t$. The left and right moving quasiparticle excitations of the two halves form multiple segmented light-cone hydrodynamics that display ballistic transport of the conserved charge densities and currents in different degrees of freedom. Our analytical results provide a deep understanding of the quantum transport of multi-component Luttinger liquids in quantum systems with both bosonic and fermionic statistics., Comment: 6+13 pages, 3 figures, a few new references were added

We investigate the wave packet dynamics for a one-dimensional incommensurate optical lattice with a special on-site potential which exhibits the mobility edge in a compactly analytic form. We calculate the density propagation, long-time survival probability and mean square displacement of the wave packet in the regime with the mobility edge and compare with the cases in extended, localized and multifractal regimes. Our numerical results indicate that the dynamics in the mobility-edge regime mix both extended and localized features which is quite different from that in the mulitfractal phase. We utilize the Loschmidt echo dynamics by choosing different eigenstates as initial states and sudden changing the parameters of the system to distinguish the phases in the presence of such system., Comment: 16 pages, 8 figures

In this work, we present a reinforcement learning algorithm that can find a variety of policies (novel policies) for a task that is given by a task reward function. Our method does this by creating a second reward function that recognizes previously seen state sequences and rewards those by novelty, which is measured using autoencoders that have been trained on state sequences from previously discovered policies. We present a two-objective update technique for policy gradient algorithms in which each update of the policy is a compromise between improving the task reward and improving the novelty reward. Using this method, we end up with a collection of policies that solves a given task as well as carrying out action sequences that are distinct from one another. We demonstrate this method on maze navigation tasks, a reaching task for a simulated robot arm, and a locomotion task for a hopper. We also demonstrate the effectiveness of our approach on deceptive tasks in which policy gradient methods often get stuck., Comment: 8 pages, Accepted ICML 2019